Numerical simulation of some viscoelastic fluids

Numerical simulation of the Oldroyd-B type viscoelastic fluids is a very challenging problem. rnThe well-known High Weissenberg Number Problem" has haunted the mathematicians, computer scientists, and rnengineers for more than 40 years. rnWhen the Weissenberg number, which represents the ratio of elasticity to viscosity, rnexceeds some limits, simulations done by standard methods break down exponentially fast in time. rnHowever, some approaches, such as the logarithm transformation technique can significantly improve rnthe limits of the Weissenberg number until which the simulations stay stable. rnrnWe should point out that the global existence of weak solutions for the Oldroyd-B model is still open. rnLet us note that in the evolution equation of the elastic stress tensor the terms describing diffusive rneffects are typically neglected in the modelling due to their smallness. However, when keeping rnthese diffusive terms in the constitutive law the global existence of weak solutions in two-space dimension rncan been shown. rnrnThis main part of the thesis is devoted to the stability study of the Oldroyd-B viscoelastic model. rnFirstly, we show that the free energy of the diffusive Oldroyd-B model as well as its rnlogarithm transformation are dissipative in time. rnFurther, we have developed free energy dissipative schemes based on the characteristic finite element and finite difference framework. rnIn addition, the global linear stability analysis of the diffusive Oldroyd-B model has also be discussed. rnThe next part of the thesis deals with the error estimates of the combined finite element rnand finite volume discretization of a special Oldroyd-B model which covers the limiting rncase of Weissenberg number going to infinity. Theoretical results are confirmed by a series of numerical rnexperiments, which are presented in the thesis, too.

Oxide thermoelectrics via a glass-ceramic route

Thermoelektrizität beschreibt die reversible Beeinflussung und Wechselwirkung von Elektrizität und Temperatur T in Systemen abseits des thermischen Gleichgewichtes. In diesen führt ein Temperaturgradient entlang eines thermoelektrischen Materials zu einem kontinuierlichen Ungleichgewicht in der Energieverteilung der Ladungsträger. Dies hat einen Diffusionsstrom der energiereichen Ladungsträger zum kalten Ende und der energiearmen Ladungsträger zum heißen Ende zur Folge. Da in offenen Stromkreisen kein Strom fließt, wird ein Ungleichgewicht der Ströme über das Ausbilden eines elektrischen Feldes kompensiert. Die dadurch entstehende Spannung wird als Seebeck Spannung bezeichnet. Über einen geeigneten Verbraucher, folgend aus dem Ohm'schen Gesetz, kann nun ein Strom fließen und elektrische Energie gewonnen werden. Den umgekehrten Fall beschreibt der sogenannte Peltier Effekt, bei dem ein Stromfluss durch zwei unterschiedliche miteinander verbundene Materialien ein Erwärmen oder Abkühlen der Kontaktstelle zur Folge hat. Die Effizienz eines thermoelektrischen Materials kann über die dimensionslose Größe ZT=S^2*sigma/kappa*T charakterisiert werden. Diese setzt sich zusammen aus den materialspezifischen Größen der elektrischen Leitfähigkeit sigma, der thermischen Leitfähigkeit kappa und dem Seebeck Koeffizienten S als Maß der erzeugten Spannung bei gegebener Temperaturdifferenz. Diese Arbeit verfolgt den Ansatz glaskeramische Materialien mit thermoelektrischen Kristallphasen zu synthetisieren, sie strukturell zu charakterisieren und ihre thermoelektrischen Eigenschaften zu messen, um eine Struktur-Eigenschaft Korrelation zu erarbeiten. Hierbei werden im Detail eine elektronenleitende (Hauptphase SrTi_xNb_{1-x}O_3) sowie eine löcherleitende Glaskeramik (Hauptphase Bi_2Sr_2Co_2O_y) untersucht. Unter dem Begriff Glaskeramiken sind teilkristalline Materialien zu verstehen, die aus Glasschmelzen durch gesteuerte Kristallisation hergestellt werden können. Über den Grad der Kristallisation und die Art der ausgeschiedenen Spezies an Kristallen lassen sich die physikalischen Eigenschaften dieser Systeme gezielt beeinflussen. Glaskeramiken bieten, verursacht durch ihre Restglasphase, eine niedrige thermische Leitfähigkeit und die Fermi Energie lässt sich durch Dotierungen in Richtung des Leitungs- oder Valenzbands verschieben. Ebenso besitzen glaskeramische Materialien durch ihre Porenfreiheit verbesserte mechanische Eigenschaften gegenüber Keramiken und sind weniger anfällig für den Einfluss des Sauerstoffpartialdruckes p_{O_2} auf die Parameter. Ein glaskeramisches und ein gemischt keramisch/glaskeramisches thermoelektrisches Modul aus den entwickelten Materialien werden konzipiert, präpariert, kontaktiert und bezüglich ihrer Leistung vermessen.

Non-parametric estimation of the diffusion coefficient of a branching diffusion with immigration

Wir betrachten Systeme von endlich vielen Partikeln, wobei die Partikel sich unabhängig voneinander gemäß eindimensionaler Diffusionen [dX_t = b(X_t),dt + sigma(X_t),dW_t] bewegen. Die Partikel sterben mit positionsabhängigen Raten und hinterlassen eine zufällige Anzahl an Nachkommen, die sich gemäß eines Übergangskerns im Raum verteilen. Zudem immigrieren neue Partikel mit einer konstanten Rate. Ein Prozess mit diesen Eigenschaften wird Verzweigungsprozess mit Immigration genannt. Beobachten wir einen solchen Prozess zu diskreten Zeitpunkten, so ist zunächst nicht offensichtlich, welche diskret beobachteten Punkte zu welchem Pfad gehören. Daher entwickeln wir einen Algorithmus, um den zugrundeliegenden Pfad zu rekonstruieren. Mit Hilfe dieses Algorithmus konstruieren wir einen nichtparametrischen Schätzer für den quadrierten Diffusionskoeffizienten $sigma^2(cdot),$ wobei die Konstruktion im Wesentlichen auf dem Auffüllen eines klassischen Regressionsschemas beruht. Wir beweisen Konsistenz und einen zentralen Grenzwertsatz.

Three-year follow-up of human transplanted kidneys by diffusion-weighted MRI and blood oxygenation level-dependent imaging

To prospectively determine the 3-year stability and potential changes of functional parameters in renal allograft recipients obtained from diffusion-weighted imaging (DWI) and blood oxygenation level-dependent (BOLD) MRI.

Restricted or severely hindered diffusion of intramyocellular lipids in human skeletal muscle shown by in vivo proton MR spectroscopy

Although magnetic resonance spectroscopy can be used as a unique tool to study molecular diffusion, it is rarely used to measure the diffusion properties of intramyocellular and extramyocellular lipids. Lipids have very low apparent diffusion coefficients (ADCs), which make these measurements difficult and necessitate strong diffusion gradients and long diffusion times. Consequence is that these measurements have inherently low signal-to-noise ratio and are prone to artifacts. The addition of physiological triggering and individual storage and processing of the spectra is seen to be a possible approach to maximize signal intensity and achieve high reproducibility of the experiments. Thus, the optimized measurement protocol was used to investigate the diffusion properties of lipids in human skeletal muscle in vivo. At a diffusion time of about 110 ms, intramyocellular lipids show a significantly lower ADC (2.0 × 10(-6) mm(2)/s, 95% confidence interval 1.10 × 10(-6) to 2.94 × 10(-6) mm(2)/s) than extramyocellular lipids (1.58 × 10(-5) mm(2)/s, 95% confidence interval 1.41 × 10(-5) to 1.75 × 10(-5) mm(2)/s). Because the chemical properties of both lipid pools can be assumed to be similar, the difference can only be attributed to restricted or severely hindered diffusion in the intramyocellular droplets.

I know what I like: Stability of aesthetic preference in Alzheimer's disease

Two studies explored the stability of art preference in patients with Alzheimer’s disease and age-matched control participants. Preferences for three different styles of paintings, displayed on art postcards, were examined over two sessions. Preference for specific paintings differed among individuals but AD and non-AD groups maintained about the same stability in terms of preference judgments across two weeks, even though the AD patients did not have explicit memory for the paintings. We conclude that aesthetic responses can be preserved in the face of cognitive decline. This should encourage caregivers and family to engage in arts appreciation activities with patients, and reinforces the validity of a preference response as a dependent measure in testing paradigms.

Au@Hg nanoalloy formation through direct amalgamation: Structural, spectroscopic, and computational evidence for slow nanoscale diffusion

Dynamic core-shell nanoparticles have received increasing attention in recent years. This paper presents a detailed study of Au-Hg nanoalloys, whose composing elements show a large difference in cohesive energy. A simple method to prepare Au@Hg particles with precise control over the composition up to 15 atom% mercury is introduced, based on reacting a citrate stabilized gold sol with elemental mercury. Transmission electron microscopy shows an increase of particle size with increasing mercury content and, together with X-ray powder diffraction, points towards the presence of a core-shell structure with a gold core surrounded by an Au-Hg solid solution layer. The amalgamation process is described by pseudo-zero-order reaction kinetics, which indicates slow dissolution of mercury in water as the rate determining step, followed by fast scavenging by nanoparticles in solution. Once adsorbed at the surface, slow diffusion of Hg into the particle lattice occurs, to a depth of ca. 3 nm, independent of Hg concentration. Discrete dipole approximation calculations relate the UV-vis spectra to the microscopic details of the nanoalloy structure. Segregation energies and metal distribution in the nanoalloys were modeled by density functional theory calculations. The results indicate slow metal interdiffusion at the nanoscale, which has important implications for synthetic methods aimed at core-shell particles.

Apparent diffusion coefficient in the aging mouse brain: a magnetic resonance imaging study

Novel magnetic resonance imaging sequences have and still continue to play an increasing role in neuroimaging and neuroscience. Among these techniques, diffusion-weighted imaging (DWI) has revolutionized the diagnosis and management of diseases such as stroke, neoplastic disease and inflammation. However, the effects of aging on diffusion are yet to be determined. To establish reference values for future experimental mouse studies we tested the hypothesis that absolute apparent diffusion coefficients (ADC) of the normal brain change with age. A total of 41 healthy mice were examined by T2-weighted imaging and DWI. For each animal ADC frequency histograms (i) of the whole brain were calculated on a voxel-by-voxel basis and region-of-interest (ROI) measurements (ii) performed and related to the animals' age. The mean entire brain ADC of mice <3 months was 0.715(+/-0.016) x 10(-3) mm2/s, no significant difference to mice aged 4 to 5 months (0.736(+/-0.040) x 10(-3) mm2/s) or animals older than 9 months 0.736(+/-0.020) x 10(-3) mm2/s. Mean whole brain ADCs showed a trend towards lower values with aging but both methods (i + ii) did not reveal a significant correlation with age. ROI measurements in predefined areas: 0.723(+/-0.057) x 10(-3) mm2/s in the parietal lobe, 0.659(+/-0.037) x 10(-3) mm2/s in the striatum and 0.679(+/-0.056) x 10(-3) mm2/s in the temporal lobe. With advancing age, we observed minimal diffusion changes in the whole mouse brain as well as in three ROIs by determination of ADCs. According to our data ADCs remain nearly constant during the aging process of the brain with a small but statistically non-significant trend towards a decreased diffusion in older animals.

The role of circumferential fiberotomy in enhancing orthodontic stability

Objectives: Circumferential septal fiberotomy (CSF) following orthodontic treatment has been propagated to improve stability and prevent relapse of tooth alignment. The hypothesis of no difference between performed CSF and controls was tested. Methods: In 9 consecutively admitted patients at the end of orthodontic tooth alignment, the lower arch-wire was removed. CSF was performed from the mandibular canine to the central incisor on a randomly chosen side, while the contra-lateral side served as unsurgerized control. At baseline and every 4 weeks up to 6 months, study casts were taken and 1) analyzed using the Irregularity Index (II)according to Little and 2)photographed, traced and superimposed digitally. The translational and rotational movements of teeth as well as gingival parameters were analyzed as well. Results: By using the II and by superimposing the tracings, no statistically significant differences were found between the test (CSF) and control sides for any parameters. Moreover, CSF did not impinge on the gingival tissues. Conclusion: Since CSF did not improve stability of orthodontically aligned teeth nor prevent relapse during the healing pahse of up to 6 months, CSF should not be recommended following orthodontic therapy.

Cerebral connectivity and psychotic personality traits : A diffusion tensor imaging study

This study aims to investigate the relationship between regional connectivity in the brain white matter and the presence of psychotic personality traits, in healthy subjects with psychotic traits. Thirteen healthy controls were administered the MMPI-2, to assess psychotic traits and, according to MMPI results, a dichotomization into a group of "high-psychotic" and "low-psychotic" was performed. Diffusion tensor imaging (DTI) was used as a non-invasive measure, in order to obtain information about the fractional anisotropy (FA), an intravoxel index of local connectivity and, by means of a voxelwise approach, the between-group differences of the FA values were calculated. The "high-psychotic" group showed higher FA in the left arcuate fasciculus. Subjects with low scores for psychotic traits had significantly higher FA in the corpus callosum, right arcuate fasciculus, and fronto-parietal fibers. In line with previous brain imaging studies of schizophrenia spectrum disorders, our results suggest that psychotic personality traits are related to altered connectivity and brain asymmetry.

Characterization of white matter alterations in phenylketonuria by magnetic resonance relaxometry and diffusion tensor imaging

A multimodal MR study including relaxometry, diffusion tensor imaging (DTI), and MR spectroscopy was performed on patients with classical phenylketonuria (PKU) and matched controls, to improve our understanding of white matter (WM) lesions. Relaxometry yields information on myelin loss or malformation and may substantiate results from DTI attributed to myelin changes. Relaxometry was used to determine four brain compartments in normal-appearing brain tissue (NABT) and in lesions: water in myelin bilayers (myelin water, MW), water in gray matter (GM), water in WM, and water with long relaxation times (cerebrospinal fluid [CSF]-like signals). DTI yielded apparent diffusion coefficients (ADCs) and fractional anisotropies. MW and WM content were reduced in NABT and in lesions of PKU patients, while CSF-like signals were significantly increased. ADC values were reduced in PKU lesions, but also in the corpus callosum. Diffusion anisotropy was reduced in lesions because of a stronger decrease in the longitudinal than in the transverse diffusion. WM content and CSF-like components in lesions correlated with anisotropy and ADC. ADC values in lesions and in the corpus callosum correlated negatively with blood and brain phenylalanine (Phe) concentrations. Intramyelinic edema combined with vacuolization is a likely cause of the WM alterations. Correlations between diffusivity and Phe concentrations confirm vulnerability of WM to high Phe concentrations.

Heat transfer in microwave heating

Heat transfer is considered as one of the most critical issues for design and implement of large-scale microwave heating systems, in which improvement of the microwave absorption of materials and suppression of uneven temperature distribution are the two main objectives. The present work focuses on the analysis of heat transfer in microwave heating for achieving highly efficient microwave assisted steelmaking through the investigations on the following aspects: (1) characterization of microwave dissipation using the derived equations, (2) quantification of magnetic loss, (3) determination of microwave absorption properties of materials, (4) modeling of microwave propagation, (5) simulation of heat transfer, and (6) improvement of microwave absorption and heating uniformity. Microwave heating is attributed to the heat generation in materials, which depends on the microwave dissipation. To theoretically characterize microwave heating, simplified equations for determining the transverse electromagnetic mode (TEM) power penetration depth, microwave field attenuation length, and half-power depth of microwaves in materials having both magnetic and dielectric responses were derived. It was followed by developing a simplified equation for quantifying magnetic loss in materials under microwave irradiation to demonstrate the importance of magnetic loss in microwave heating. The permittivity and permeability measurements of various materials, namely, hematite, magnetite concentrate, wüstite, and coal were performed. Microwave loss calculations for these materials were carried out. It is suggested that magnetic loss can play a major role in the heating of magnetic dielectrics. Microwave propagation in various media was predicted using the finite-difference time-domain method. For lossy magnetic dielectrics, the dissipation of microwaves in the medium is ascribed to the decay of both electric and magnetic fields. The heat transfer process in microwave heating of magnetite, which is a typical magnetic dielectric, was simulated by using an explicit finite-difference approach. It is demonstrated that the heat generation due to microwave irradiation dominates the initial temperature rise in the heating and the heat radiation heavily affects the temperature distribution, giving rise to a hot spot in the predicted temperature profile. Microwave heating at 915 MHz exhibits better heating homogeneity than that at 2450 MHz due to larger microwave penetration depth. To minimize/avoid temperature nonuniformity during microwave heating the optimization of object dimension should be considered. The calculated reflection loss over the temperature range of heating is found to be useful for obtaining a rapid optimization of absorber dimension, which increases microwave absorption and achieves relatively uniform heating. To further improve the heating effectiveness, a function for evaluating absorber impedance matching in microwave heating was proposed. It is found that the maximum absorption is associated with perfect impedance matching, which can be achieved by either selecting a reasonable sample dimension or modifying the microwave parameters of the sample.

Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

Diffusion tensor imaging of two unrelated Chinese men with hereditary spastic paraplegia associated with thin corpus callosum

Hereditary spastic paraplegia (HSP) associated with thin corpus callosum is a rare autosomal recessive neurodegenerative disorder characterized by an abnormally thin corpus callosum, normal motor development, slowly progressive spastic paraparesis and cognitive deterioration. To investigate and localize abnormalities in the brains of two Chinese patients with HSP-TCC, with mutations in the spatacsin gene. Diffusion tensor imaging (DTI) was used to determine the mean diffusion (MD) and fractional anisotropy (FA) in the brains of the patients in comparison to 20 healthy subjects. Voxel-based analysis (VBA) of both the diffusion and anisotropy values were performed using statistical parametric mapping (SPM). Significant changes with MD increase and FA reduction were found in the already known lesions including the corpus callosum, cerebellum and thalamus. In addition, changes were also found in regions that appear to be normal in conventional MRI, such as the brain stem, internal capsule, cingulum and subcortical white matter including superior longitudinal fascicle and inferior longitudinal fascicle. Neither increase in FA nor reduction in MD was detected in the brain. Our study provides clear in vivo MR imaging evidence of a more widespread brain involvement of HSP-TCC. MD is more sensitive than FA in detecting lesions in thalamus and subcortical white matter, suggesting that MD may be a better marker of the disease progression.

Influence of Mechanical and Thermal Boundary Conditions on Stabilizing/Destabilizing Mechanisms in Evaporating Liquid Films

Liquid films, evaporating or non-evaporating, are ubiquitous in nature and technology. The dynamics of evaporating liquid films is a study applicable in several industries such as water recovery, heat exchangers, crystal growth, drug design etc. The theory describing the dynamics of liquid films crosses several fields such as engineering, mathematics, material science, biophysics and volcanology to name a few. Interfacial instabilities typically manifest by the undulation of an interface from a presumed flat state or by the onset of a secondary flow state from a primary quiescent state or both. To study the instabilities affecting liquid films, an evaporating/non-evaporating Newtonian liquid film is subject to a perturbation. Numerical analysis is conducted on configurations of such liquid films being heated on solid surfaces in order to examine the various stabilizing and destabilizing mechanisms that can cause the formation of different convective structures. These convective structures have implications towards heat transfer that occurs via this process. Certain aspects of this research topic have not received attention, as will be obvious from the literature review. Static, horizontal liquid films on solid surfaces are examined for their resistance to long wave type instabilities via linear stability analysis, method of normal modes and finite difference methods. The spatiotemporal evolution equation, available in literature, describing the time evolution of a liquid film heated on a solid surface, is utilized to analyze various stabilizing/destabilizing mechanisms affecting evaporating and non-evaporating liquid films. The impact of these mechanisms on the film stability and structure for both buoyant and non-buoyant films will be examined by the variation of mechanical and thermal boundary conditions. Films evaporating in zero gravity are studied using the evolution equation. It is found that films that are stable to long wave type instabilities in terrestrial gravity are prone to destabilization via long wave instabilities in zero gravity.